Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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COROLLARIE.
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>Hence it is manifeſt, that Sections of the ſame River (which
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are no other than the vulgar meaſures of the River) have
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betwixt themſelves reciprocal proportions to their veloci
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ties; for in the firſt Propoſition we have demonſtrated that the
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Sections of the ſame River, diſcharge equal quantities of Water
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in equal times; therefore, by what hath now been demonſtrated
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the Sections of the ſame River ſhall have reciprocal proportion
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to their velocities; And therefore the ſame running water chan
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geth meaſure, when it changeth velocity; namely, increaſeth the
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meaſure, when it decreaſeth the velocity, and decreaſeth the
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meaſure, when it increaſeth the velocity.</
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>On which principally depends all that which hath been ſaid
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above in the
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Diſcourſe,
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and obſerved in the
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Corollaries
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and
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Ap
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pendixes
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; and therefore is worthy to be well underſtood and
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heeded.</
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>PROPOSITION IV.</
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If a River fall into another River, the height of the
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firſt in its own Chanel ſhall be to the height that it
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ſhall make in the ſecond Chanel, in a proportion
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compounded of the proportions of the breadth of
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the Chanel of the ſecond, to the breadth of the
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Chanel of the firſt, and of the velocitie acquired in
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the Chanel of the ſecond, to that which it had in
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its proper and first Chanel.
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>Let the River A B, whoſe height is A C, and breadth C B,
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that is, whoſe Section is A C B; let it enter, I ſay, into a
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nother River as broad as the line E F, and let it therein make
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the riſe or height D E, that is to ſay, let it have its Section in
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the River whereinto it falls D E F; I ſay, that the height A C
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hath to the height D E the proportion compounded of the pro
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portions of the breadth E F, to the breadth C B, and of the ve
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locity through D F, to the velocity through A B. </
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<
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>Let us ſup
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poſe the Section G, equal in velocity to the Section A B, and in
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breadth equal to E F, which carrieth a quantity of Water e
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qual to that which the Section A B carrieth, in equal times,
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and conſequently, equal to that which D F carrieth. </
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<
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>Moreover,
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as the breadth E F is to the breadth C B, ſo let the line H be to </
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